My company (a dedicated Oracle shop) and I have used Oracle Portal for many years and have been very successful with it. But I have to warn you against taking on this task if you do not have experience with PL/SQL (Oracle's proprietary database programming language).
An intranet built on Oracle Portal is likely to make extensive use of custom-built "portlets". You can build these in Java or PL/SQL; in my experience, 95% of all real-life portlets are built using PL/SQL.
Theoretically, if you use the latest version of Oracle Portal (10.1.4), you can consume WSRP 1.0 portlets. So if you can build portlets in .NET that will communicate using WSRP 1.0, you could integrate these. But if your customer asks for "support", they probably expect you to be able to tweak their existing portlets - and that would require PL/SQL programming experience.
There's a fairly good description of Oracle Portal on the Oracle Wiki:
http://wiki.oracle.com/page/Oracle+Portal
Strategically, Oracle has placed Oracle Portal is in the "Continue & Converge" category, which means that it's supported and will receive minor updates. Their strategic portal product these days is Oracle WebCenter, but that's a $125,000 per CPU behemoth; it's likely to be overkill for 99% of all sites built on Oracle Portal.